From Euclid to GG-6

Abstract

For 2300 years, the ideal of physical science has been Euclid's: a deductive system in which every theorem follows from a few postulates, with nothing left to fit. Modern physics drifted from that ideal — the Standard Model carries some 28 free parameters, general relativity adds Newton's constant and the cosmological constant, and string theory answers with a landscape of 10⁵00 vacua, in which the values are selected rather than derived. This foundations volume of the Arisaka-GG series argues that the drift was not necessary. Building on the GG-Constitution, the 6D bulk, and the modified Bianchi identity BI-6, it shows that the dimensionful content of physics is exhausted by the Geometric Universal Five Constants GU-5 = , G_N, ℏ; k_B, Q_B — three conversion factors of the bulk directions of one six-dimensional geometry and two of its boundary projection — while its dimensionless content is exhausted by the five OGN-5 integers (1,3,5; 7,35), Diophantine theorems of the same geometry. The elementary charge e is not a primitive but a consequence of α⁻¹(0) = 2^J + N² = 137, leaving only the mathematical constants e (Euler) and π to complete the inventory, with no continuous parameter intervening. The volume establishes the reconstruction theorems and the master parameter audit, importing — rather than re-deriving — the Standard-Model and cosmological results of its companion papers. After all, the Euclidean condition is what makes a physical theory worth the name deductive science: every quantity must be either a conversion factor of the geometry or a theorem of the framework, never a free choice. The 2300-year detour from Euclid is, in this precise sense, ending.